I wouldn't like to say there's anything wrong with the
analytical abilities of either player - what we have here is and
error of judgement. My guess is, it's a quiet position in a solid
opening, and neither player bothered to look.

Chess is a tense game. This tension may make you want to
believe things that aren't really true, and comfort yourself with
things that mean you don't have to think too hard any more. Not a
bit of it....

Black has a hopeless, passive position, just as he has had for the
last umpteen moves. Petrosian just went

1. Rxh6

which was met by

1...f3!

Hoping for 2. Kxf3 Kg7discovered
check, winning the rook.

2. Kg5 Ke8 White resigns, unable to
catch the f-pawn.

Afterwards, Petrosian explained that a move like ...f3
just didn't fit with "Black's hopeless position". But
where there's life, there's hope!

"For a long time I had regarded my position as a
winning one. Thus the whole opening phase of the struggle, when
Korchnoi was unable to get out of trouble, had psychologically
attuned me to the idea that the ending would be favourable to me
... and here comes the oversight 35 Rxh6?? I did
not even see the threat ...f4-f3, possibly because it was in
contrast to Black's hopeless position. Personally, I am of the view
that if a strong master does not see such a threat at once he will
not notice it, even if he analyses the position for twenty or
thirty minutes." - PETROSIAN.

I have a whole book full of these types of disaster, when
one player just turned the alarm off. You should be on guard all
the time, with the alarm dial turned up to 11!

Please note that Petrosian was also thinking less than
objectively about the game, and thinking only about his plans. Your
opponent also has a right to exist...

It used to be thought that there wasn't much difference in the
abilities of strong and weak players at analysis - rather, it was
all about judgement and experience. There might not be a lot of
difference between GMs and IMs, but there is increasing evidence
that among we club players, there are large and important
differences.

Here White gets carried away with his attacking
possibilities, when unflappable Exeter player Brian Hewson calmly
sidesteps the main line of a sacrifice (11...fxe6) threatening a
pin on the e-file.

and won. It is often the case that players will analyse
one line very deeply but fail to spot an early alternative - as
mentioned above, Grandmaster Kotov advised many years ago to
identify each candidate move at the outset before
analysing any one move deeply. Had White done this he could
not fail to notice the possibility of Black castling, and
should then spot the classic pattern of Q and K lined up on the
e-file which suggests a pin from a Black R on e8.

The situation in this Candidates' Match game is tense Although
White undoubtedly holds the advantage, Moscow players analysing
while the game was going on could find no clear continuation, e.g.
26. Nd5 Qe6! and Black holds.

26. Qb6

Surprising and elegant, this 'creeping move' impressed
many, including Kotov who has cited it more than once. The move
prepares to answer ...Qe6 with Bxc5 and leads to a swift win. To
Kotov, this was a far more brilliant move than the Queen sacrifice
that ended the game.

You have probably seen either the British Chess
Magazine column Find the Winning Continuation, or
the same idea in Chess magazine, called there
Winning Combinative Play. There are also books of tactical
positions for solving, one I quite liked for the basics was Chernev
and Reinfeld, Winning Chess.

After that, you get serious. More testing (literally) is
the Chess magazine feature, How Good is your
Chess? which takes you through a real game and gives you
points (There is a book of these under the same name by Danny King;
BCM have a similar feature called Test Your Chess.) Here's
an easy example of such a test:

This is all 'practice makes perfect' style with little
explanation. The theory of candidate moves and trees
of analysis I found in Kotov, Think like a
Grandmaster (a summary is also to be found in Kotov, Plan
like a Grandmaster). This book also describes how Kotov used
to analyse complicated master games, writing down his conclusions
for comparison. Both books give test positions with a full tree of
analysis.

Another important book for theory is Nunn and Griffiths,
Secrets of Grandmaster Play. It is a deliberately
educative book, showing, firstly, what a complete analysis of a
game looks like, but also giving lots of practical tips and
observations, and trying to show how much players really see at the
board.

And lastly, there are some good ideas in Dvoretsky,
Secrets of chess tactics. In particular, he describes the
technique of playing-out of positions for which an analysis has
been published. For example, he played on from the following
positions from the Nunn/Griffiths book with his pupils (Yusupov and
Dolmatov) as if the position had arisen in a game against the
clock. This is a realistic test and you can check your conclusions
against what Nunn has analysed.

"I can see the combinations as well as Alekhin, I
just cannot get into the same positions" -- SPIELMANN

Quotes

(another personal favourite)" A combination composed of a sacrifice has more immediate effect upon the person playing over the game in which it occurs than another combination, because the apparent senselessness of the sacrifice is convincing proof of the design of the player offering it.